• Honam Mathematical Journal
• /
• v.43 no.2
• /
• pp.209-219
• /
• 2021

We define a new concept of module amenability which is compatible with original definition of amenability. For a module dual algebra 𝓐, we will show that if every module derivation D : 𝓐** → J𝓐**⊥ is inner then 𝓐 is weak module amenable. Moreover, we will prove that under certain conditions, weak module amenability of 𝓐** implies weak module amenability of 𝓐.

• The Pure and Applied Mathematics
• /
• v.25 no.3
• /
• pp.203-218
• /
• 2018

An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.

• Journal of Electrical Engineering and information Science
• /
• v.2 no.4
• /
• pp.92-98
• /
• 1997

This paper presents a new approach to obtaining a reduced-order model for multi-module converters. The proposed approach can be used to derive the reduced-order model for a wide class of multi-module converters including pulse-width-modulated (PWM) converters, soft-switched PWM converters, and resonant converters. The reduced-order model has the structure of a conventional single-module converter while preserving the dynamics of the original multi-module converter. Derivation procedures and the use of the reduced-order model is demonstrated using a three-module boost converter.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.801-812
• /
• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• Honam Mathematical Journal
• /
• v.43 no.1
• /
• pp.68-77
• /
• 2021

This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.

• Kyungpook Mathematical Journal
• /
• v.32 no.3_spc
• /
• pp.635-642
• /
• 1992

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.663-673
• /
• 2010

This work was intended as an attempt to introduce and investigate the Connes-amenability of module extension of dual Banach algebras. It is natural to try to study the $weak^*$-continuous derivations on the module extension of dual Banach algebras and also the weak Connes-amenability of such Banach algebras.

• The Journal of the Korea Contents Association
• /
• v.3 no.3
• /
• pp.40-46
• /
• 2003

In the paper, designed digital contents security module to check unlawfulness reproduction and distribution of digital contents. This paper applied Diffie-Hellman algorithm that use discrete logarithm and random number as primary for public key application to create encryption key that agree each other through communication channel between DCPS and HOST, and applied Triple DES repeat DES 3 times through 2 different encryption key that is selecting ANSI X9.17 that is key management standard, ISO 8732 and PEM(Privacy-Enhanced Mail) etc. by secondary protection for safe transmission of digital contents in transmission line. Designed security module consist of key exchange module, key derivation module and copy protection processing module. Digital contents security module that design in this thesis checks reproduction and distribution of digital contents by unauthenticated user through user certification function and digital contents encryption function, and protect digital contents transmission line.

• Proceedings of the Korea Contents Association Conference
• /
• 2003.11a
• /
• pp.245-248
• /
• 2003

We construct a universal derivation module of an R-algebra which is constructed by means of a tensor product of three copies of the algebras.

• Journal of the Chungcheong Mathematical Society
• /
• v.2 no.1
• /
• pp.81-90
• /
• 1989

Let $D:C^n(I){\longrightarrow}M$ be a derivation from the Banach algebra of n times continuously differentiable functions on an interval I into a Banach $C^n(I)$-module M. If D is continuous and D(z) is contained in the k-differential subspace, the image of D is contained in the k-differential subspace. The question of when the image of a derivation is contained in the k-differential subspace is discussed.